Baseball's All-Time Best Hitters: How Statistics Can Level the Playing Field

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Tony Gwynn is the greatest hitter in the history of baseball. That's the conclusion of this engaging and provocative analysis of baseball's all-time best hitters. Michael Schell challenges the traditional list of all-time hitters, which places Ty Cobb first, Gwynn 16th, and includes just 8 players whose prime came after 1960. Schell argues that the raw batting averages used as the list's basis should be adjusted to take into account that hitters played in different eras, with different rules, and in different ballparks. He makes those adjustments and produces a new list of the best 100 hitters that will spark debate among baseball fans and statisticians everywhere.

Schell combines the two qualifications essential for a book like this. He is a professional statistician—applying his skills to cancer research—and he has an encyclopedic knowledge of baseball. He has wondered how to rank hitters since he was a boy growing up as a passionate Cincinnati Reds fan. Over the years, he has analyzed the most important factors, including the relative difficulty of hitting in different ballparks, the length of hitters' careers, the talent pool that players are drawn from, and changes in the game that raised or lowered major-league batting averages (the introduction of the designated hitter and changes in the height and location of the pitcher's mound, for example). Schell's study finally levels the playing field, giving new credit to hitters who played in adverse conditions and downgrading others who faced fewer obstacles. His final ranking of players differs dramatically from the traditional list. Gwynn, for example, bumps Cobb to 2nd place, Rod Carew rises from 28th to 3rd, Babe Ruth drops from 9th to 16th, and Willie Mays comes from off the list to rank 13th. Schell's list also gives relatively more credit to modern players, containing 39 whose best days were after 1960.

Using a fun, conversational style, the book presents a feast of stories and statistics about players, ballparks, and teams—all arranged so that calculations can be skipped by general readers but consulted by statisticians eager to follow Schell's methods or introduce their students to such basic concepts as mean, histogram, standard deviation, p-value, and regression. Baseball's All-Time Best Hitters will shake up how baseball fans view the greatest heroes of America's national pastime.

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Editorial Reviews

New York Times
[A] trenchant attempt to reorder the hierarchy. . . . [Schell's] calculations produce a new all-time greatest hitter, revealed in sometimes breathless prose.
— Joseph Kahn
Mathematical Association of America Online Book Review
[Schell] has provided a wealth of baseball trivia and statistics. The style of writing is engaging and often lively and, in fact, encourages continued debate over the data and conclusions presented. The text will undoubtedly become a part of the baseball statistics fan's library.
— Randall J. Swift
Buried deep within every true baseball fan is a nerd with a scorecard and a calculator. . . . To refute those who say players from different eras can't be compared because they played in different circumstances, Schell levels the playing field by building models to account for those varying circumstances: ballparks, pitching quality, night games, etc. . . . His conclusions are often surprising but well substantiated.
The Los Angeles Times
Altogether, a good read. . . .
— Earl Gutskey
New York Times - Joseph Kahn
[A] trenchant attempt to reorder the hierarchy. . . . [Schell's] calculations produce a new all-time greatest hitter, revealed in sometimes breathless prose.
Mathematical Association of America Online Book Review - Randall J. Swift
[Schell] has provided a wealth of baseball trivia and statistics. The style of writing is engaging and often lively and, in fact, encourages continued debate over the data and conclusions presented. The text will undoubtedly become a part of the baseball statistics fan's library.
The Los Angeles Times - Earl Gutskey
Altogether, a good read. . . .
From the Publisher
"[A] trenchant attempt to reorder the hierarchy. . . . [Schell's] calculations produce a new all-time greatest hitter, revealed in sometimes breathless prose."—Joseph Kahn, New York Times

"[Schell] has provided a wealth of baseball trivia and statistics. The style of writing is engaging and often lively and, in fact, encourages continued debate over the data and conclusions presented. The text will undoubtedly become a part of the baseball statistics fan's library."—Randall J. Swift, Mathematical Association of America Online Book Review

"Buried deep within every true baseball fan is a nerd with a scorecard and a calculator. . . . To refute those who say players from different eras can't be compared because they played in different circumstances, Schell levels the playing field by building models to account for those varying circumstances: ballparks, pitching quality, night games, etc. . . . His conclusions are often surprising but well substantiated."Booklist

"[Schell] ranks current player Tony Gwynn as the best all-time hitter, well ahead of the modern batting king, Ted Williams, and no doubt outraging the ghosts of Ty Cobb and Babe Ruth. . . . All in all, this book is for the hardcore baseball fan. . . ."Library Journal

"Altogether, a good read. . . ."—Earl Gutskey, The Los Angeles Times

Joseph Kahn
Michael J. Schell, a biostatistician at the University of North Carolina and a lifelong baseball fan, has tried to rewrite history. He argues that raw batting averages are meaningful only to compare hitters playing in the same park at the same time with the same competition, not to rank superstars in the Hall of Fame. Mr. Schell's new book is a trenchant attempt to reorder the hierarchy using methods like those he applies to cancer research. He submitted batting averages of history's top baseball players to a gantlet of tests. He makes adjustments for the changing baseball talent pool, in part because blacks and other minorities were once excluded from the major leagues. He also tries to eliminate the distorting effects of quirky ball parks, end-of-career slumps and rule changes. The resulting list rocks conventional wisdom. It also takes the numerology among baseball fans to a new level of obsessiveness.
New York Times
Earl Gustsky
Schell, a biostatistics professor at the University of North Carolina, is also a lifelong baseball buff who applies statistical methods to "level the playing field" between the baseball eras to arrive at a ranked list of the game's 100 greatest hitters. And the winner is . . . Tony Gwynn. Factoring in elements such as turn-of-the-century ballparks, rule changes, hitter-friendly ballparks, hitter-unfriendly eras, on-base percentage, and an added, fascinating factor--base-on-balls percentage. Gwynn, Schell's number-crunching shows, emerges with an "adjusted" career average of .342, with Ty Cobb next at .340 and Rod Carew third at .332.
Los Angeles Times
Library Journal
Schell (biostatistics, Univ. of North Carolina), a professional statistician, here turns his attention from his field of health science to a lighter but more contentious subject, baseball. The rating of players has been an unending argument among diehard fans and specialists, such as those dedicated aficionados of the Society for American Baseball Research, which has given statistical debate more credibility. Now this book from Princeton University Press is a signal that the academics have entered the fray, too. Schell's book, however, makes some strange claims. He ranks current player Tony Gwynn as the best all-time hitter, well ahead of the modern batting king, Ted Williams, and no doubt outraging the ghosts of Ty Cobb and Babe Ruth. Schell's statistics "level" the playing field because they downplay the importance of power, thus favoring Gwynn. Schell is on more solid ground when he proposes players who should be included in the Hall of Fame. All in all, this book is for the hardcore baseball fan, especially one comfortable with complex statistical analysis. For comprehensive baseball collections.--Paul M. Kaplan, Lake Villa Dist. Lib., IL
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Product Details

  • ISBN-13: 9780691123431
  • Publisher: Princeton University Press
  • Publication date: 3/7/2005
  • Pages: 328
  • Sales rank: 1,340,090
  • Product dimensions: 5.36 (w) x 8.24 (h) x 0.78 (d)

Meet the Author

Michael Schell is Professor of Biostatistics at the University of North Carolina and Director of the Biostatistics Core Facility at the Lineberger Comprehensive Cancer Center. He is the author of "Baseball's All-Time Best Sluggers: Adjusted Batting Performance from Strikeouts to Home Runs" (Princeton) and has published more than 100 research articles on statistics and cancer.
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Read an Excerpt

Baseball's All-Time Best Hitters

How Statistics Can Level the Playing Field

By Michael J. Schell


Copyright © 1999 Michael J. Schell
All rights reserved.
ISBN: 978-1-4008-5063-1


On Deck with the Qualifying Players

We're in the on deck circle, getting ready to bat. Before we undertake the four adjustments needed to identify the top 100 hitters in baseball history, we need to warm up a little. We'll do this by looking at the players from which the top 100 hitters will emerge. In the introduction, we identified these players. They are called qualifying players—836 players who, through the 1997 season, have had at least 4000 at bats and have retired from baseball or who have had at least 8000 at bats, regardless of their retirement status.

Who are these players? We know at least that their managers rated their abilities highly. After all, they couldn't have had 4000 at bats unless their manager penciled their name onto the lineup card day after day. Did the game change over the years, leading managers to favor different types of players in different eras? Let's find out.

Batting Average

Managers clearly want players who can hit for average. Figure 1.1 shows the percentage of qualifying players in 10-point groups. For example, 18% of the players batted between .260 and .269. The averages range from .218 for George McBride to .366 for Ty Cobb. The average of the batting averages of all qualifying players is .279, with three-quarters of the players hitting between .250 and .299.

George McBride was the regular shortstop for the Washington Senators from 1908 to 1916. McBride earned his keep by being an excellent fielder. The shortstop position is the place where managers are most willing to give up batting points for good fielding.

Cobb was ... well, if you don't know yet, it's high time you learned! Ty Cobb was the aggressive, spike sharpening centerfielder for the Detroit Tigers. According to baseball reference books, he is credited with having the highest lifetime average of all time. He won 10 to 12 batting titles (more about this later) in a 13-year stretch from 1907–19. He was also a great base stealer, resulting from a potent combination of speed and spike. In recent years, several books have been written about him and one was made into a movie entitled simply Cobb.

Picture Cobb and McBride as contrasting bookends in the fortunes of baseball. They faced each other on the field 22 times a year for 9 years. Cobb's shortstop teammate was Donie Bush, a lifetime .250 hitter who walked a lot. Cobb also had shared the outfield with fellow Hall of Farner Sam Crawford, a .309 hitter with the highest lifetime number of triples. McBride's teammate in centerfield was Clyde Milan, a .285 hitter. Chick Gandil, who averaged .293 for the Senators from 1912 to 1915, was the only other "decent" hitter on McBride's team. From 1908–11, Detroit won two league titles and averaged 91 wins in 154-game seasons. Washington averaged 60 wins, finishing 7th or 8th each year in an 8-team league. Just as you might expect. From 1912–16, however, Detroit slipped to 80 wins a year, in spite of adding .310-hitting Bobby Veach in 1914–and Washington passed by them, averaging 85 wins.

How was this possible? Two explanations come to mind. First, Detroit had the best hitter's park in the American League at that time, while Washington had the worst. So perhaps the batting average differences weren't so great as they seem (more about this later). Second, Washington had Walter "Big Train" Johnson on the mound for them, who didn't need a lot of runs to eke out wins for his team. Johnson is considered by many to have been the greatest pitcher ever. Interesting—Johnson was able to take a team with the weakest "qualifying" hitter and still outwin Detroit, a team with the game's best hitter. Clark Griffith, the owner of the Washington Senators, tried to hire Cobb away from the Tigers. Baseball history would surely have been changed greatly if Cobb and Johnson had played on the same team!

At Bats

When baseball players are listed by decreasing number of at bats, the best players seem to be at the top. Why is this? The primary reason seems to be that better hitters are likely to stay in the lineup and hence have longer careers with more at bats. Figure 1.2 shows the percentage of players with a given range of at bats and their average batting average. The number of players drops dramatically as the number of at bats increases. Their batting averages go up 2 to 7 points for each additional 1000 at bats.

Table 1.1 shows representative retired players in the different at bat groups who primarily played after 1972. For the first column of names, one player was chosen for each at bat group starting alphabetically with the A's. For the second column of names, the selections started with the M's. While this is a very small sample of players, it illustrates the point that better hitters tend to have more at bats.

Batting Handedness

Although most batters are right-handed, 34% are left-handers. This is much higher than the percentage of those who write left-handed in the U.S. population, which is about 10% according to the World Book Encyclopedia. Left-handers bat 14 points higher than right-handers who, in turn, bat 3 points higher than switch-hitters (Fig. 1.3).


Pete Rose started his career at second base, moved to the outfield, then to third base, and finally to first base. So what position should be given for Rose? The Baseball Encyclopedia and Total Baseball both require a player to play at least 1000 games at a position in order to qualify for it, and we will do the same. If a player does not qualify at a position, he qualifies as a utility player if he plays at least 500 games in his non-primary position. Otherwise, he qualifies at no position. Let's take a look at some examples.

Pete Rose played 1327 games in the outfield, 939 at first base, 634 at third, and 628 at second. He qualifies as an outfielder.

Jackie Robinson played 751 games at second base, 256 games at third base, 197 games at first base, 152 games in the outfield, and I game at shortstop. Since Robinson did not qualify at his primary position —second base—and played 606 games in non-primary positions, he qualifies as a utility player.

Frank Chance, the first baseman in the famed Chicago Cub double play combo "Tinker to Evers to Chance," played 997 games at first base, 186 games as a catcher, and 72 games in the outfield. He fell three games short of qualifying at first base and qualifies at no position. Most of the players who qualify at "no position" had fewer than 5000 career at bats (Chance had 4299 AB).

Only three players qualify at two different positions. Stan Musial played 1896 games in the outfield and 1016 games at first base. We will consider Musial to be an outfielder. Ernie Banks played 1259 games at first base and 1125 games at shortstop. Even though he played more games at first, we will consider Banks to be a shortstop, since he is usually placed with the shortstop lists. Harold Baines qualifies both as an outfielder and a designated hitter (DH), but has played more games as a DH and will be counted there.

The designated hitter was only established in 1973 and is used only by the American League. As a result, a scant 3 players qualify to date—Harold Baines, Don Baylor, and Hal McRae. (Paul Molitor also has had over 1000 games as a designated hitter. However, he has been "qualified" as a utility player since he played extensively at third, second, and first base, which certainly showed his "utility" to the team in the field.)

Figure 1.4 shows the percentage of qualifying players and overall player batting averages at each position. Outfielders and first basemen bat more than 10 points higher than the other positions (excluding the DHs). Shortstops and catchers, at the two most demanding defensive positions, have the lowest batting averages.

Decade of Mid-Career

Baseball is often divided into eras depending on the dominant features of play. Sports Encyclopedia: Baseball divides baseball history into 6 eras (although some of the era names are mine): the 19th century era (1876–1900); "dead ball" era (1901–19); "lively ball" era (1920–45); post–World War II era (1946–60); expansion era (1961–72); and designated hitter era (1973–present).

A player's performance is usually better understood in the light of when he played. Ty Cobb played from 1905–28—in both the "dead ball" and "lively ball" eras. The mid-career year gives a snapshot summary of when a player played. The mid-career year is the year when the player attained half of his total career at bats. Cobb had 11,434 career at bats, so his mid-career year, 1916, occurred when he attained his 5717th at bat.

Batting averages vary greatly by the decade of mid-career of ballplayers, with the overall averages among the players ranging from the upper .260s in the 1960–80s to .295 in the 1920–30s, as Figure 1.5 shows. This variation of nearly 30 points is quite substantial. The big rise in the 1920s partly explains why the era from 1920–45 is often called the "lively" ball period. Many baseball writers claim that a livelier ball was introduced in 1920, although other writers dispute the claim. I will discuss the variation in batting averages over time in greater detail in chapter 3.

The drop in the number of players whose mid-careers were in the 1940s was due to the military service of players during World War II. An average of 27 players per team (including pitchers) missed at least one full season, serving tours of duty sometime between 1942 and 1945. These 427 players missed an average of 2.4 full seasons. These players had shortened careers and some never returned to baseball.

Looking at Pairs of Player Characteristics

We have seen how hitters' batting averages differ by four hitter characteristics —how many at-bats they had, what handedness they had, what position they played, and when they played. Sometimes new insights arise when looking at pairs of characteristics. Four pairs will now be presented.

Batting Handedness and Position

We saw earlier that 34% of the players are left-handed. This percentage, however, varies considerably by position. Figure 1.6 shows that while the majority of outfielders and first basemen are left-handed, very few shortstops are. In fact, there are only 4 left-handed shortstops, and the last, Arky Vaughan, was in mid-career in 1938! Also, note that the middle infield (2B and SS) have higher percentages of switch-hitters than the other positions.

We saw earlier that left-handed batters hit 14 points better than right-handed batters. However, Figure 1.7 shows that the difference ranges from 3–8 points for most positions and the exceptions—short-stops, second basemen, and third basemen—do not have many left-handed hitters. How can this be? This paradox is largely due to the fact that the positions with the best hitters overall—the outfield and first base—have the highest percentage of left-handed hitters.

Position by position, right-handers bat several points better than switch-hitters. Thus, apparently players become switch-hitters to become competitive with more gifted single-handed players.

Batting Handedness and Decade of Mid-Career

Figure 1.8 shows the major shifts in batting handedness over baseball history. In 1880–89, the first full decade of major league baseball, only 24% of the players were left-handed and none were switch-hitters. By the 1890s, 36% of the players were left-handed and 6% were switch-hitters. Those percentages remained relatively constant until 1970, when the percentage of switch-hitters climbed from 6% to 13%, with a corresponding decrease in left-handed hitters.

Position and At Bats

Figure 1.9 shows the job "insecurity" of catchers. Catchers represent 9% of the players with careers of between 4000 and 5999 at bats. The percentage drops to 5% for the 6000–7999 at bat group and a scant 2% of players with 8000 or more at bats. The most "secure" infield position is shortstop.

Why do catchers and shortstops have such different prospects? Mter all, both are highly skilled positions defensively and shortstops hit even less than catchers. Clearly, the strain of catching takes a severe toll.

Utility players and players who don't qualify at a position ("None") tend to have fewer at bats. This is built into the very definitions of the categories since, given enough at bats, a player will qualify somewhere (Fig. 1.9).

Position and Decade of Mid-Career

From 1890 to the present, the percentages of qualifying players at different positions have been relatively constant. However, the percentages were quite different in 1880–89. None of the early players qualified as a catcher and only one—Jack Glassock—qualified as a shortstop. On the other hand, 28% did not qualify at a position ("None") and 20% qualified as utility players. Two reasons for the high percentages at these two "positions" is that players in the 1880s played fewer games and changed positions much more often. It is surprising how quickly the position profile settled down to a constant pattern (Fig. 1.10).

An Analysis of the Traditional Top 100 Hitters List

Of the players in the traditional top 100 hitters list presented in the introduction (Table I), 59 are outfielders and 15 are first basemen, while at most 6 players play at any of the other positions. There are 59 left-handers, quite a bit higher than the overall rate of 34%. The most striking feature, however, is the decade when these hitters were in mid-career.

The mid-career year for each of the top hitters is given in Table I. The top 100 hitters are concentrated in a couple of decades, quite different from the percentage of qualifying players overall by decade of mid-career, as Figure 1.11 shows.

Almost half of the traditional top 100 hitters were in mid-career between 1920–39, although only 17% of the qualifying players played then. Moreover, only 8 top hitting players were in mid-career after 1960, although 41 % of all batters played then. Visually, these percentages look quite different. We might raise the question whether these differences are due to chance alone or whether there is some identifiable "association" between the decade of mid-career and being a top 100 hitter. This can be answered using a chi-square test.

The chi-square p-value to test for the association of the decade of mid-career and being a top 100 hitter is less than .0001. Thus, the evidence is quite strong that the percentage of players by decade of mid-career of traditional top 100 hitters does not closely match the percentage of qualifying hitters overall.

Stepping Up to the Plate

Four adjustments—for late career batting declines, hitting feasts and famines, the talent pool, and ballpark effects—are needed to level the playing field for batting averages. A basic assumption behind these adjustments is that there is an equal proportion of hitters who are "great" across baseball history. Consequently, one would reasonably expect the percentages of qualifying players that are "true" top 100 hitters to be fairly constant across the decades. We have just seen that this is not the case for the traditional top hitter list. We will see progressive improvement in the "constancy" over the four adjustments to batting averages (both graphically and by having a p-value above .05 for the chi-square test for the association between the decade of mid-career and being a top 100 hitter).

The traditional top 100 hitters account for 451 single-year top 5 finishes, including 125 batting championships. These numbers are impressive at first blush. However, nine of the players never finished in the top 5 in hitting in any year and 30 others had only 1 or 2 top 5 finishes. We will see improvements in these totals after the proposed adjustments.

In the next four chapters we will examine each of the four adjustments in turn, see why it is needed, learn how to make it, and discover what its effects are. Just like a ballplayer—we'll reach home only after touching each of the bases.


Excerpted from Baseball's All-Time Best Hitters by Michael J. Schell. Copyright © 1999 Michael J. Schell. Excerpted by permission of PRINCETON UNIVERSITY PRESS.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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Table of Contents

List of Figures
List of Tables
Technical Notes
Introduction: In the Dugout 3
Pt. I The Method 13
1 On Deck with the Qualifying Players 15
2 First Base - Adjusting for Late Career Declines 29
3 Second Base - Adjusting for Hitting Feasts and Famines 45
4 Third Base - Adjusting for League Batting Talent 67
5 Home - Adjusting for Ballpark 103
Pt. II The Findings 133
6 The Adjusted Top 100 Hitters 135
7 Top Hitters by Position 157
8 Best Single-Season Batting Averages 173
9 The Ballparks 185
10 On Base Percentage 213
11 The Hall of Fame 227
12 Where Would the Current Stars Rank? 241
Afterword: Post-Game Wrap-Up 249
App. I: Abbreviations and Glossary 253
App. II Right- vs. Left-Handed Hitting 257
App. III League Batting Averages 259
App. IV Ballpark Effect Batting Averages 269
App. V League Base on Balls Averages 275
References 283
Index 285
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  • Anonymous

    Posted November 24, 2002

    Baseball's All-Time Best Hitters : How Statistics Can Level the Playing Field

    This was a great book. It addressed stars of the past & contemporary players. As written, as based on the author's formulas, it appeared that Ted Williams is the best hitter of all time. However, it was written before the explosion of Mark McGuire, Barry Bonds, Sammy Sosa and so many others lately & commonly achieving the 50 HR and such high slugging & on base plateaus.

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  • Anonymous

    Posted December 15, 2008

    No text was provided for this review.

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